Question

What is the third root of the expression ∛17? Provide step-by-step calculations.

a) ∛17 = 2.571
b) ∛17 = 3.571
c) ∛17 = 4.571
d) ∛17 = 5.571

Answer 1

The cube root of 17 is a number between 2 and 3. By using a calculator, we can determine that the approximate value of ∛17 is 2.571, making option a) the correct answer.

Step-by-step explanation:

To find the third root of the expression ∛17, also known as the cube root of 17, we want to calculate the value that, when cubed (multiplied by itself three times), gives us 17. This is typically a calculation best done with a scientific calculator, as cube roots of non-perfect cubes are not easily computed by hand.

However, to help point you in the right direction, let's take a look at the cube roots of the perfect cubes nearest to 17:

• The cube root of 8 (∛8) is 2, since 2³ = 8.
• The cube root of 27 (∛27) is 3, since 3³ = 27.

Since 17 is between 8 and 27, we know the cube root of 17 will be between 2 and 3. Using a calculator, we find that:

∛17 ≈ 2.571

Therefore, the correct answer from the given options would be:

a) ∛17 = 2.571

Keep in mind, the answer provided is an approximate value rounded to three decimal places.